Circular Motion and Gravity

Physics 201 Lecture 5

We now focus on forces that bend motion – an example is in projectile motion

Constant ForceConstant Force Central ForceCentral Force

Uniform circular motion requires a specific magnitude of net force

This represents the period of the motion

Two applications:Banked curves and the mass spectrometer

Rotating frames introduce two inertial forces

Centrifugal ForceCentrifugal Force Coriolis ForceCoriolis Force

Movement toward the rotation will push you into

the rotation

“Stationary” objects will be pushed away from the

rotation

Gravity is universal, but usually is applied to one big object

• The gravitational constant is the least accurately measured physical constant

• Astronomy cannot measure mass directly, only GM

Object GM in SI units

Sun

Earth

Moon

Weight is gravitational

• Weight is a force not due to contact – which is unusual (easy to consider it “intrinsic”)

• Using Newton’s formula, we can calculate the acceleration due to gravity

• Identification of gravity and weight is historically significant – first “unification” moment in physics

Kepler’s third law

• Consider a planet in uniform circular motion – gravity provides the centripetal force:

• This allows us to relate orbital period to mass:

• If we know the distance and the period, we can estimate mass – but measuring distance is surprisingly difficult

Applications of Kepler’s third law: Saturn’s rings and evidence for dark matter

Rings of SaturnRings of Saturn Dark MatterDark Matter

Kepler’s law will tend to tear objects apart

Kepler’s law is not valid in

galactic core

Observed speed of stars in galaxies are

too high